摘要： Induced coherence (IC) between two spatially separated but indistinguishable spontaneous parametric down conversion (SPDC) processes underpins the recent revival of nonlinear interferometry and has led to new applications in quantum imaging and mid-infrared (MIR) spectroscopy [1,2]. These applications exploit induced coherence and the spectral or spatial correlations between signal and idler photons generated through SPDC. Here, we theoretically describe the phenomenon of IC in a general way by making use of a quantum-mechanical approach based on the classical Green’s function (GF) of the system [3,4]. Our formalism is well suited for treating generic linear optical properties of a system, including loss, and studying their influence on the IC phenomena. Moreover, our approach can account for arbitrary spatial profiles of the nonlinearity and hence can be used to describe generalized IC experiments with different number of photon-pair sources. Here we propose a sensing experiment using a single nonlinear waveguide [5] and investigate IC using our formalism. We find that in this case a substance under test inside or surrounding the waveguide can affect the IC during the generation stage along the nonlinear waveguide, making this a compact scheme for MIR spectroscopy without the need for MIR detectors.